Our main interest in these differentiability concepts comes from the
fact that the functional delta method may become applicable. For (fully)
Hadamard differentiable maps this is well known; see,
e.g., [1]}.
For Hadamard directionally differentiable maps the functional
delta method is given in [2]};
recently attention to this result has been drawn for instance by [3]}
and [4]}. For convenience, we
reproduce this result as the following lemma.
